Puzzle 005 on Professor Layton and the Curious Village is called "Digital Digits". For this, you need to figure out how many times a digital clock will display 3 or more of the same number in a row (or consecutive) in one day.

Steps

1

Remember that this particular clock operates in a 12-hour display, not international/military, where it's 24 hours. To make it easier for yourself, either do the morning (midnight to noon) or afternoon/evening (noon to midnight) and then double the number for the entire day.

2

Write down the most obvious times. When we see a digital clock, we automatically think of "1:11 pm" or "4:44 am". Here would be the potential list:

1:11

2:22

3:33

4:44

5:55

3

Study the "1:11" and "2:22". Learn that the minutes will still be the same during the 11 and 12 o' clock hours and you'd still have the same 3 consecutive numbers.

11:11

12:22

4

Take the "11:11". Because you have "1" as your consecutive number, use this to your advantage and go up in minutes.

11:10

11:12

11:13

11:14

11:15

11:16

11:17

11:18

11:19

5

Think of the solid hour times. Note that "10:00" is the only hour with 3 consecutive zeros.

6

Count how many different times you have and double it. You should end up with 34 to write on the next screen.